Physics Does it matter if a physics internship is paid or not?

So, I am an undergraduate student who wasn't able to obtain a national scholarship (REU, NSERC type) for this summer. But I was able to get an internship with a professor, who needed a certain project to be done in his lab, and apparently rather desperately. However I went in with the premise that I didn't need any funding for the work and informed the professor of this. However I am still wondering if the experience would look better, such as for applying to graduate school, if it would be funded (no matter how little) by the professor. And even so, is it worth the risk of asking the professor for a few dollars an hour just to have a proof that the research project is being funded? thanks for reading

I don't think it matters. When you list this position on your resume, it's not like you're going to write "got paid $8/hr" or whatever. If you're happy not being paid, I think it would be better to stick with that, instead of causing unnecessary complication and risking losing the position.

If he's paying you through a grant like an REU it looks great. If he has to pay you out of pocket, then nobody cares. I did 4 internships like that during my undergrad and only 2 of them were paid, both times the professor paid out of pocket. When I list these internships, I don't even bother mentioning that I was paid.

Most internships you do during undergrad will probably NOT be paid. Unfortunately this is fairly standard.

So, I am an undergraduate student who wasn't able to obtain a national scholarship (REU, NSERC type) for this summer. But I was able to get an internship with a professor, who needed a certain project to be done in his lab, and apparently rather desperately. However I went in with the premise that I didn't need any funding for the work and informed the professor of this. However I am still wondering if the experience would look better, such as for applying to graduate school, if it would be funded (no matter how little) by the professor. And even so, is it worth the risk of asking the professor for a few dollars an hour just to have a proof that the research project is being funded? thanks for reading

Whether or not the position is funded only matters to you. I was a TA, and no one cared about my pay. I got in-state student rates/status for it, so was fine for me. If you are doing any significant amount of the scientific work, hopefully, you'll get mentioned in the publication. Publications do matter.